Drogba, who has scored 12 goals in as many appearances against Arsenal since joining Chelsea in 2004, was left unmarked at the far post and simply poked home captain John Terry's header from a Florent Malouda corner in the eighth minute.
His second came on the break after some sustained pressure from Arsenal, when England midfielder Frank Lampard burst out of his half in the 23rd minute, galloped 20 metres and laid the ball off to the Ivorian on the right of the Arsenal area. The big striker stepped inside Gael Clichy to ram the ball past a stranded Manuel Almunia.
Before the goal Chelsea keeper Petr Cech had had to make two saves in quick succession, diverting a ball at Samir Nasri's feet behind for a corner and blocking a shot from Andrei Arshavin with his feet as Arsenal used the speed of Nasri, Theo Walcott and the tricky Russian to harass the Chelsea defence.
But Arsene Wenger's team, so energetic in the build up, lacked the final flourish.
"My captain has a fantastic attitude. He's done very well every game for the team," Chelsea coach Carlo Ancelotti told reporters.
"It's very important to have this leadership."
Arsenal coach Arsene Wenger praised Terry's defensive qualities.
"I give credit to Chelsea for their defending. They have fantastic defenders. I believe John Terry wants to win every time he plays football. Sometimes playing can be a diversion from events off the pitch," he said.
Wenger watched mostly stony-faced as his side's title chances ebbed. Arsenal have not won the league since 2004 and last captured silverware with the FA Cup in 2005.
"Against Manchester United we did not turn up. Here, we were completely dominant," he said.
"I always thought we would come back but you have to give them credit, they defended very well. There were lots of tricks from a very experienced team."
